Mathematical clay tablet Haddad 104 was published in 1984 by Michael Roaf and Farouk Al-Rawi and it has since been considered a very important piece of evidence for the study of the mathematics of the Old Babylonian period. Its provenance is the ancient city of Me-Turan, in the region of the Diyala river, and the tablet offers a mixture of general characteristics of Mesopotamian mathematics with regional traits of the Diyala region. It brings ten problems, dealing with grain containers, measuring vessels, work load and brick making, matters with a clear empirical appeal and so with high interest for the study of measure in antiquity. In this tablet, numbers accompanied of units of measure (measure numbers) and numbers without measure units (so-called abstract numbers) are intensely employed. The literature of the field of the history of cuneiform mathematics strongly supports the interpretation that measure numbers were used to provide the data in the statement of problems and often to write the final answers, whereas abstract numbers were used in intermediate numerical calculations. The passage from one type to the other was helped by specific texts which associated them, the metrological tables. Haddad 104 is on the whole consistent with this picture, but some of its passages make the distinction between these types of numbers a blurred one, especially some conversions of length measures which seem to be made within the frame of abstract numbers. Besides, other passages show that calculations could be carried out with measure numbers as well. For example, some problems speak of “the reciprocal of 1 mina of silver” or multiply “2 by 1 sila of grain” or “1 by 1 talent of silver”. Both cases point to a differentiation of the mathematical tradition that, together with the linguistic features of this tablet, help characterise the mathematics of the Diyala region, confirming Haddad 104 as a very rich source of examples of mathematical practices related to measure and units of measure. Thus, in the present paper, I offer an analysis of its text showing that the scribe who wrote it – and by extension, the milieu where it was produced – was able to deal with measure and abstract numbers in a way that their roles could fluctuate and even overlap. From the historiographical point of view, this modulates the distinction between these numbers and enriches our knowledge of the mathematical facets of measure in Ancient Mesopotamia.